{
  "abstract": "A set \\(\\mathcal{G}\\) of integers is a \\(g\\)-Golomb ruler if each positive difference appears at most \\(g\\) times between any 2 elements of the set, and \\(G(g,n)\\) denotes the minimum diameter of such a ruler with \\(n\\) marks. We prove a general lemma for passing from certain modular constructions to ordinary \\(g\\)-Golomb rulers. The key point is that, in a modular \\(g\\)-Golomb ruler, no cyclic gap length can occur more than \\(g\\) times. This gives a larger guaranteed cut than the previous average gap argument. We apply this lemma to cyclic relative difference sets, Singer sets, Ruzsa--Spence rulers, and Paley quadratic residues to provide many competing constructions for \\(g\\)-Golomb Rulers. A computation on the grid \\(1\\le g\\le500\\), \\(n=g+b\\), \\(2\\le b\\le500\\), compares the four resulting construction families.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.07931",
  "author_total": 1,
  "authors": [
    {
      "name": "Aditya Gupta"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/53ceh20rapwk2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.07931",
  "fulltext_url": null,
  "id": "53ceh20rapwk2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.07931",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2607|Limits and Structures in Graph Theory"
    ]
  ],
  "openalex": "W7167927135",
  "pdf_url": "https://arxiv.org/pdf/2607.07931",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/53ceh20rapwk2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:37Z",
      "native_id": "2607.07931",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.07931"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Modular Constructions of g-Golomb Rulers",
  "title_text": "Modular Constructions of g-Golomb Rulers",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:31Z",
  "url": "https://research.draconitic.com/paper/53ceh20rapwk2",
  "venue": "arXiv",
  "versions": []
}